The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1
- Total numbers on wheel = total possible outcomes = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- Grey colored portion = {3}
- White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}
- X = Event that wheel stops on a white slice
- P(X) = number of white slices ÷ total number of slices
Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1
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Interest rate = 7%
I= PRT where I is the interest earned, p is the principal, r is rate as a decimal, and t is time in years.
A - P will give us the interest earned.
12,150 - 9,000 = 3,150
3150 = (9000)(r)(5)
3150 = 45,000r
r = 0.07
r = 7%
Answer: There are two solutions and they are
theta = 135
theta = 225
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Explanation:
Recall that x = cos(theta). Since the given cosine value is negative, this indicates x < 0. Theta is somewhere to the left of the y axis, placing it in quadrant 2 or quadrant 3.
It turns out there are two solutions, with one solution per quadrant mentioned above. Use the unit circle to find that the two solutions are:
theta = 135
theta = 225
You're looking for points on the unit circle that have x coordinate equal to x = -sqrt(2)/2. Those two points correspond to the angles of 135 and 225, which are in quadrants 2 and 3 respectively.
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I recommend using your calculator to note that
-sqrt(2)/2 = -0.70710678
cos(135) = -0.70710678
cos(225) = -0.70710678
The decimal values are approximate. Make sure your calculator is in degree mode. Because those three results are the same decimal approximation, this indicates that cos(135) = cos(225) = -sqrt(2)/2.
